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Endomotives of toric varieties

Jin, Zhaorong and Marcolli, Matilde (2014) Endomotives of toric varieties. Journal of Geometry and Physics, 77 . pp. 48-71. ISSN 0393-0440. https://resolver.caltech.edu/CaltechAUTHORS:20140401-134330780

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Abstract

We construct endomotives associated to toric varieties, in terms of the decomposition of a toric variety into torus orbits and the action of a semigroup of toric morphisms. We show that the endomotives can be endowed with time evolutions and we discuss the resulting quantum statistical mechanical systems. We show that in particular, one can construct a time evolution related to the logarithmic height function. We discuss relations to F_1-geometry.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.geomphys.2013.12.006DOIArticle
http://www.sciencedirect.com/science/article/pii/S0393044013002301PublisherArticle
https://arxiv.org/abs/1309.4101arXivDiscussion Paper
Additional Information:© 2014 Elsevier B.V. Received 4 October 2013. Received in revised form 10 December 2013. Accepted 14 December 2013. Available online 21 December 2013. This paper is based on the results of the first author’s summer research project, supported by a Summer Undergraduate Research Fellowship at Caltech. The second author acknowledges support from NSF grants DMS-0901221, DMS-1007207, DMS-1201512, and PHY-1205440.
Funders:
Funding AgencyGrant Number
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
NSFDMS-0901221
NSFDMS-1007207
NSFDMS-1201512
NSFPHY-1205440
Subject Keywords:Noncommutative geometry; Endomotives; Quantum statistical mechanical systems; Toric varieties; Height functions
Record Number:CaltechAUTHORS:20140401-134330780
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20140401-134330780
Official Citation:Zhaorong Jin, Matilde Marcolli, Endomotives of toric varieties, Journal of Geometry and Physics, Volume 77, March 2014, Pages 48-71, ISSN 0393-0440, http://dx.doi.org/10.1016/j.geomphys.2013.12.006. (http://www.sciencedirect.com/science/article/pii/S0393044013002301)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:44582
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:01 Apr 2014 21:04
Last Modified:03 Oct 2019 06:19

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